Abstract
A general boundary/initial value problem for a linear thermoviscoelastic solid of integral typs is posed, and a uniqueness theorem is proved which holds for both bounded and unbounded domains. In the latter case we do not impose conditions on the behaviour of the unknown fields at infinity. Mild definiteness hypotheses on the initial values of the relaxation functions are assumed throughout.
Sommario
Dopo aver formulato un problema ai limiti generale per solidi lineari termoviscoelastici di tipo integrale, si stabilisce un teorema di unicità della soluzione valido per domini limitati e per domini illimitati. In questo secondo caso non viene imposta alcuna condizione sul comportamento all'infinito delle variabili di campo; si suppongono verificate solamente certe deboli condizioni di segno sui valori iniziali di alcune funzioni di rilassamento.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Christensen, R. M., Theory of Viscoelasticity: an introduction, Academic Press, 1971.
NavarroC. B., ‘Asymptotic stability in linear thermoviscoelasticity’, J. Math. Anal. Appl., 65 (1978) 399–431.
ChelminskiK., ‘A mixed boundary value problem in linear thermoviscoelasticity’. Arch. Mech., 39 (1987) 95–102.
LucaI., ‘Implicatii termodinamice si reversibilitate temporala in termoviscoelasticitatea liniara de tip integral’, Stud. Cerc. Mec. Apl., 45 (1986) 549–578.
BorrelliA. and PatriaM. C., ‘Discontinuity waves through a linear thermo-viscoelastic solid of integral type’. Internat. J. Non-Linear Mech. 26 (1991) 141–150.
BorrelliA. and PatriaM. C., ‘General analysis of discontinuity waves in thermoviscoelastic solids of integral type’ Il Nvoro Cimento, 106 B (1991) 213–224.
GurtinM. E. and PipkinA. C., ‘A general theory of heat conduction with finite wave speeds’, Arch. Rational Mech. Anal., 31 (1968) 113–126.
Morro, A., ‘Termodinamica del non equilibrio ed equazioni costitutive’ in: Propagazione del calore ed equazioni costitutive, Quaderni del C.N.R.-Gruppo Nazionale per la Fisica Matematica, 1984.
WheelerL., ‘On the uniqueness of solutions to the displacement problem in linear elastodynamics’, J. Elasticity, 1 (1971) 121–124.
FinnJ. M. and WheelerL. T., ‘Wave propagation aspects of the generalized theory of heat conduction, Z. Angew. Math. Phys., 23 (1972) 927–939.
LucaI., ‘Domain of influence and uniqueness in viscothermoelasticity of integral type’, Continuum Mech. Thermodyn. 1 (1989) 213–226.
Luca, I., ‘A uniqueness theorem in anisotropic viscothermoelasticity of integral type (submitted to Archive of Mechanics).
Gurtin, M. E., ‘The linear theory of elasticity’ in: Handbuch der Physik, Bd. VIa/2, 1972.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Borrelli, A., Patria, M.C. Uniqueness in boundary/initial value problems for a thermoviscoelastic solid of integral type. Meccanica 26, 143–147 (1991). https://doi.org/10.1007/BF00429881
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00429881